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Theorem ltrel 9695
Description: 'Less than' is a relation. (Contributed by NM, 14-Oct-2005.)
Assertion
Ref Expression
ltrel  |-  Rel  <

Proof of Theorem ltrel
StepHypRef Expression
1 ltrelxr 9694 . 2  |-  <  C_  ( RR*  X.  RR* )
2 relxp 4962 . 2  |-  Rel  ( RR*  X.  RR* )
3 relss 4942 . 2  |-  (  <  C_  ( RR*  X.  RR* )  ->  ( Rel  ( RR*  X. 
RR* )  ->  Rel  <  ) )
41, 2, 3mp2 9 1  |-  Rel  <
Colors of variables: wff setvar class
Syntax hints:    C_ wss 3442    X. cxp 4852   Rel wrel 4859   RR*cxr 9673    < clt 9674
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-v 3089  df-un 3447  df-in 3449  df-ss 3456  df-pr 4005  df-opab 4485  df-xp 4860  df-rel 4861  df-xr 9678  df-ltxr 9679
This theorem is referenced by:  dflt2  11447  gtiso  28121  ballotlemimin  29164
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